Update: It looks like the problem has been solved in a timely manner. Everyone can get back at their games, as PSN works just fine now.
PlayStation Network is currently down worldwide, as errors NW 31194-8 and/or NW-31201-7 are shown every time someone tries to log into the online service. While Sony states on their official website that the service is in fact online, we got several reports indicating the contrary.
If you do have problems signing into PSN, please let us know. We’ll be updating this post throughout the day.